Spectral estimates of least energy solutions to the Brezis–Nirenberg problem with a variable coefficient

Abstract

Let u ε be a least energy solution to the Brezis-Nirenberg problem:is the critical Sobolev exponent and ε > 0 is a small parameter.We prove several asymptotic estimates of eigenvalues λ i,ε and corresponding eigenfunctions v i,ε to the eigenvalue problem:as ε → 0, for i = 1, 2, . . . , N + 1, N + 2.